On separation axioms in L-fuzzy topological spaces

A new concept of Hausdorff separation in an L-fuzzy topological space is defined and investigated. With respect to it, several nice properties are obtained. For instance, Hausdorff space implies T-1; Hausdorff space is proved to be hereditary, topological invariant and L-good extend. Furthermore, it is proved that an L-fuzzy topological space is Hausdorff space if and only if every molecular net has at most one limit.